Correlated rigidity percolation in fractal lattices
Correlated rigidity percolation in fractal lattices
复制标题
分形晶格中的相关刚性渗流
DOI：
10.1103/physreve.103.012104
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Mao, Xiaoming
中科院分区：
文献类型：
--
作者：
Machlus, Shae;Zhang, Shang;Mao, Xiaoming
刚性逾渗（RP）是网络中机械稳定性的出现。出于实验观察到的胶体凝胶和无序的纤维网络等材料的分形性质，我们研究RP在分形网络中的颗粒位置的内在相关性是由分形迭代控制。具体来说，我们计算的Sierpienski垫片（SG）的站点稀释晶格的临界填充分数与不同程度的分形迭代。我们的研究结果表明，虽然这些晶格的RP的相关长度指数和分形维数是相同的规则的三角形晶格，由于网络的分形性质的临界体积分数是显着降低。此外，我们开发了一个简化的SG晶格的脆弱性分析的基础上，一个单一的SG模型。该简化模型为全分形晶格的临界填充分数提供了一个上界，分形晶格的无序平均RP阈值严格遵守该上界。我们的研究结果描述了超低密度分形网络的刚性。
Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network where intrinsic correlations in particle positions is controlled by the fractal iteration. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultralow-density fractal networks.